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He also tells how his dormant mathematical instincts were
again aroused to full creative power. 'But for the persistence of
a student of this University [Johns Hopkins] in urging upon me
his desire to study with me the modern Algebra, I should never
have been led into this investigation. ... He stuck with perfect
respectfulness, but with invincible pertinacity, to his point.
He would have the New Algebra (Heaven knows where he had
heard about it, for it is almost unknown on this continent), that
or nothing. I was obliged to yield, and what was the conse-
quence? In trying to throw light on an obscure explanation in
our text-book, my brain took fire. I plunged with requickened
zeal into a subject which I had for years abandoned, and found
food for thoughts which have engaged my attention for a con-
siderable time past, and will probably occupy all my powers of
contemplation advantageously for several months to come.'
Almost any public speech or longer paper of Sylvester's con-
tains much that is quotable about mathematics in addition to
technicalities. A refreshing anthology for beginners and even
for seasoned mathematicians could be gathered from the pages
of his collected works. Probably no other mathematician has so
transparently revealed his personality through his writings as
has Sylvester. He liked meeting people and infecting them with
his own contagious enthusiasm for mathematics. Thus he says,
truly in his own case, 6So long as a man remains a gregarious
and sociable being, he cannot cut himself off from the gratifica-
tion of the instinct of imparting what he is learning, of propa-
gating through others the ideas and impressions seething in his
own brain, without stunting and atrophying his moral nature
and drying up the surest sources of his future intellectual
As a pendant to Cayley's description of the extent of modern
mathematics, we may hang Sylvester's beside it. *I should be
sorry to suppose that I was to be left for long in sole possession
of so vast a field as is occupied by modern mathematics.
Mathematics is not a book confined within a cover and bound
between brazen clasps, whose contents it needs only patience to
ransack; it is not a mine, whose treasures may take long to
reduce into possession, but which fill only a limited number of